Cycles: sharper transition from transparent to opaque areas when using partly transparent texture
You were on the right track: you can use a math node in between the alpha output of your texture and the mix shader. set it to "less than" and input a number between 0 and 1.
if you input 1, only 100% opaque pixels will be diffuse, all other pixels are glass.

Here is the node setup (I used transparent and emission shaders for demonstration purposes. this works with your node setup as well), the texture I used and the result: